Elasticity Visualization System for Mineral Analysis

1. A Visualization System For Mineral Elasticity Richard Perkins

2. Introduction • Objectives: • To continue development on the interactive elasticity visualization system • To interactively visualize elastic constants and wave velocities-direction data of crystals with different pressures, temperatures and compositional factors • To support remote visualization • Client-Server architecture approach • To support an online data repository

3. Definitions • Elasticity/Elastic • When a material is elastic it deforms under stress but return to its original state when the stress is removed • Elastic constants (Cij’s) • The relation between stress and strain as defined in Hooke’s Law • Used to define the elasticity of a crystal as a multivariate physical quantity • Wave velocity-direction data • Calculated from the elastic constants and wave propagation direction using Cristoffel’s equation • Produces three sets of wave velocities-direction data: a longitudinal wave parallel to the propagation direction and two shear waves perpendicular to the propagation direction • Anisotropic factors • Are used to compare the velocities of the different waves

4. Plots • Star plots and parallel plots • Used to directly represent the elastic constants • An-plot • Plots anisotropy factors for longitudinal and shear waves • Polygon-base surface rendering • Graphically represent the three waves (one longitudinal and two shear waves)

6. Polygon-based surface Rendering • How waves are rendered • Use an icosahedron in which each vertex on the surface represents a propagation direction • Recursively subdivide triangles into 4 triangle thereby increasing the number of vertexes • Use the wave velocity-direction data calculated from Cristoffel’s equation to figure out each velocity at each vertex (propagation direction) • Re-position the vertices in 3D space to represent the velocity-direction distribution.___

7. 1st Degree 80 triangles 2nd Degree 320 triangles 3rd Degree 1280 triangles 4th Degree 5120 triangles

8. Velocity-direction Features • Features pertaining to wave velocity-direction rendering • Views • 3d velocity • XY/YZ/ZX plane • Frame • Solid/wire • Shading • Enables/Disabled/Scaled • Axis • Degree

10. Other Features • Personalized line color and thickness • Single and Multiple mode • Temperature and pressure • Zooming • Clear screen • Removal of data from screen • Data being visualized is selected in tree • Manipulation of star plot which include: • Changing axes • Removing axes • Rotating axes • … And many more

11. Conclusion • Our system allows us to visualize elastic constants and wave velocities as a function of pressure, temperature and composition • Our system visualizes the data through the use of star plots, parallel plots, an-plots, and polygon-based surface rendering

12. Future Prospects • Make remote application access more user friendly • Expand the database • Extend the visualization system to polycrystalline and multiphase composites • Make the visualization system more user interactive